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By J. C. Fisher, J. H. Hollomon, David Turnbull

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By David Turnbull, J. H. Hollomon, J. C. Fisher

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By J. Rourke, F. S. Minshall, E. G. Zukas, C. M. Fowler, O&apos

The Hugoniot curves were determined for Fe-Si alloys containing up to 7 wt pct (13 at. pct) Si. The pressure of the transition increased as the silicon content of the alloy increased. Single crystals of 2.9 wt pct Si-Fe were also studied. The pressure of the transition was not dependent on crystallo-graphic orientation. All of the Neumann bands (mechanical twins) were attributable to (112) planes but not all of the {112} planes showed twin markings. A thorough study of the iron Hugoniot (the relationship between specific volume and pressure) under plane wave shock loading revealed a pressure transition at about 130 kbar shock pressure. The results of this investigation were reported by Bancroft, Peterson, and inshall1 in 1956. At the time of this discovery, it was felt that this was probably the a, to y transition normally found in iron and many of its alloys. Subsequently a number of iron alloy systems were surveyed in which the alloying element has a considerable effect on the normal a, to y transformation. The influence of carbon and nickel and/or chromium have already been reported.2,3 At the present time, there appears to be some doubt that this pressure transition is the usual a, to y transition In this study, Fe-Si alloys containing up to 7 wt pct (13 at. pct) Si were chosen for several reasons. To the present, the transition has been found only in iron-base alloys which were originally in the a, phase (bcc). Secondly, the y loop at atmospheric pressure extends to only about 2.5 wt pct Si. If the transition were a, to y, then one might expect a rather drastic pressure effect for alloys containing more than 2.5 wt pct Si. Finally, single crystals of Fe-Si alloys large enough for shock loading studies are readily available thereby making it quite easy to determine the effect of crystal orientation on the transition pressure and on the twinning behavior of the alloy. EXPERIMENTAL PROCEDURE Fe-Si alloys containing up to 7 wt pct Si were produced by normal vacuum casting procedures. Single crystals of Fe-2.9 wt pct Si were purchased from Monocrystals Co., Cleveland, Ohio. The orientations of these crystals were determined and samples cut so that the shock wave would be parallel (to within 1.5 deg) to either the (loo), (Ill), or (112) principal orientations. Three distinct experimental testing techniques were used. First, the pin technique, described elsewhere,4 was used to determine the transition pressure for the polycrystalline alloys as well as for the (111) and (112) orientations of the 2.9 wt pct Si single crystals. Secondly, the recovery studies, described in detail in an earlier paper,2 were used for determining the effect of alloy composition and crystal orientation on the plastic II compression-plastic I rarefaction interaction zone for several specific shock pressures. Finally, measurements of pressures above the two-wave threshold were made on the polycrystalline alloys so that more complete Hugoniot curves could be constructed for this alloy system. The optical techniques described by Rice et al.5 were used to measure the shock and free surface velocities of the samples from which the Hugoniot data were obtained. This method is applicable only in the single wave region, since velocities are obtained from the measured total transit times of the disturbances through measured sample thicknesses.

Jan 1, 1963

By Luis Salazar

Internal improvements are the great seals; stamping upon the history of nations their epochs of peace, in which notable enterprises are conceived, and fresh impulses given along the path of progress. Such forerunners of national benefits have never been so notable in Mexico as in the last four decades of the nineteenth century, during which the national faith in the consolidation of peace has been a guaranty of the development of all the elements of national prosperity. Among all the improvements which have been realized with the unanimous approbation of the people, the railroads occupy a preferred place, for upon them depends the expansion of commerce, of agriculture and of mining, the three great factors of the wealth of Mexico. In a country so extensive as the Mexican Republic, where the inhabitants are greatly scattered, and great distances separate the producer from the consumer, the only way to encourage home industry, and the development of commerce, agriculture and mining, is to construct railroads, which shorten distance, facilitate transportation and minimize its costs. The mountainous character of the country makes the navigation of its rivers practically impossible, except very near to

Jan 1, 1902

By A. W. Edelen

THE Teziutlan copper-zinc deposit is supposed to be of late Cambrian or early Paleozoic age. The country rocks are a series of schists or phyllites, flat lying and in the form of a plunging anticline. The ore deposit occupies a single horizon in the schist for a known horizontal extent of 1200 meters. Along its strike occur four large lenses or ore bodies. These ore bodies occupy positions along the flank and extend to the crest of the anticline. The primary mineralization is in the form of quartz, pyrite, sphalerite, chalcopyrite and galena, with a few scattered silver anti-monides. Quartz and pyrite form the mineralization between the ore lenses. In the ore lenses the sulphides appear as a massive, very fine-grained intergrowth of minerals. The intergrowth suggests a contemporaneous deposition of the heavy sulphides. The grain size, usually under 0.09 mm., makes the separation difficult and fine grinding important. The ore bodies were formed at great depth by solutions probably originating in the same basic magma that gave rise to the dolerite sills that are so common in their vicinity.

Jan 1, 1937

By John Hillman

Reconstruction of the British mining industry began shortly after nationalization in 1947 and continued until well into the 1950s with the support of the government. This support diminished as plentiful supplies of cheap oil from the Middle East made many coal mines uneconomic. The planned rundown which followed was foreshadowed in the 1965 White Paper which outlined financial measures to speed the closure of uneconomic collieries. The decline appeared likely to continue into the 21st century as the role of coal in UK energy requirements became less and less significant. This policy was well on course in 1973 when the oil crisis led to a complete reappraisal of the position. A government examination in 1974 of the coal industry then supported the National Coal Board's general strategy of major capital investment as set out in its 'Plan for Coal'. The plan was aimed at halting the intended decline in the industry's capacity and restoring it to 120 million tons of deep mined output in 1985. The plan proposed action along the following lines: Increase output by major investment in construction at existing collieries with sufficient reserves to give 13 million tons per annum extra output.

Jan 1, 1980

By Benjamin N. Webber

During World War II the Pocos de Caldas bauxite deposits of Minas Gerais in Brazil yielded some 60,000 tons. Since then they have maintained a small but almost continuous production. Known for many years, the deposits have been reconnoitered by a number of geologists,1-4 but no dimensional study has been possible because there have not been enough exposures to show clearly the depth, bedrock, and habit of occurrence. The deposits are somewhat unorthodox in their occurrence mainly on steep slopes of mountainous terrain. Although the parent rocks are a sequence of alkalic intrusions that bauxitize readily under the proper conditions, bauxitization has not been the dominant weathering process in the area. It is limited to certain localities where important volumes of bauxite have formed by laterization of several rock types, each yielding a distinctive type of bauxite. Bauxitization may be observed in several stages and in both direct and indirect cycles of formation. The deposits are unique in being of demonstrably recent age, so that the conditions under which the bauxite formed are essentially those of the present time. The bauxitization sequence is postulated in Fig. 1.

Jan 8, 1959

E. E. BACH, Ellsworth, Pa.-A personal interview with a man is one factor in reducing labor turnover; his working conditions is another, while the conditions under which lie brings up his family is still another; all have much to do with the reduction of labor turnover. A man well placed, happy in his work and happy in his home, will stay put and incidentally decrease the labor turnover in any industry. C. R. HOOK, Middletown, Ohio.-I am so deeply and sincerely interested in the employment problem, that it is very difficult for me, once I get started, to know when to, stop. In the first place, I want you to understand that I realize that what may be a possible accomplishment in the plant with which I happen to be connected, may not be possible of accomplishment in the same way in your plant. Our problems might be quite different; our location might be quite different, and therefore our employment problem would be very much affected by the community conditions. Two of our plants happen to be located in a town of about

Jan 4, 1918

By T. Suganuma

Mitsubishi-Cominco Smelting Co. is a joint venture of Mitsubishi Metal Mining Co. Ltd. (M.M.M.) of Japan and Cominco Ltd. of Canada. The smelter, which is located alongside M.M.M.'s Naoshima copper smelter, was completed in May, 1966 and has a capacity of 36 000 metric tons per year of refined lead. The concentrate feed for the smelter from Pine Point Mines Ltd. is high grade with low impurities; particularly silver, bismuth, antimony, and arsenic, which facilitated a simple plant layout and operation. Concentrate, fluxes, recycle granulated slag and return sinter are drawn from bins by automatic control over weigh belt feeders, sintering is carried out on a 20 m2 Lurgi updraught sintering machine, furnacing in a 3.0 m x 1 ½ m water jacketed blast furnace equipped with an Asarco continuous tapper, refining in four 120 metric ton kettles and casting on a 25 metric ton/hour automatic casting machine. The S@ gas from sintering is cleaned in a high temperature baghouse utilizing glass bags and is then delivered to the M.M.M. copper smelter acid plants. The furnace gases after cleaning in a low temperature baghouse are vented to atmosphere.

Jan 1, 1970

By Earl Oliver

Page A.I.M.E. Stabilization Committee Activity................. 133 Definition of Capture Rule: Robert E. Hardwicke.......................... 134 Westmoreland Natural Gas Co. vs. DeWitt................ 135 Kelly vs. Ohio Oil Co......................... 135 Bernard vs. Monongahela Gas Co.................... 136 Definition of Ownership in Place..................... 137 Prospective Stabilization Remedies.................... 137 Dean Roscoe Pound's Four Teats of Practicability.............. 137 I. Mechanically Feasible....................... 138 Capture Rule.......................... 138 Ownership in Place....................... 140 Mechanical Separatio.7 Method................. 140 Engineering Appraisal Method................. 141 II. Economically Advisable...................... 143 Capture Rule.......................... 144 Ownership in Place....................... 144 III. Politically Wise.......................... 144 Capture Rule..........................144 Ownership in Place.......................147 IV. Legally Sound..........................148 Capture Rule..........................148 Ownership in Place.......................149 Dean Henry M. Bates' Analysis......................149 Raumé................................152 The A.I.M.E. Stabilization Committee was named in 1932 to ascertain whether some practical substitute could be devised for the Rule of Capture, which was generally credited with being the major cause of instability in the Petroleum Industry. After considerable intercommittee correspondence a letter was received from E. DeGolyer under date of Jan. 25. 1935. in which he discussed the possibility of modifying rather than discarding the Rule of Capture. He summarized his proposal as follows:

Jan 1, 1937

Jan 1, 1891

By L. P. Teas

In spite of the influx of operators into the Gulf Coast anxious to retrieve their depleted production in other fields, and in spite of very active application of the most scientific geophysical methods to locate new producing areas, the results have been very discouraging and the year has failed to produce more than the average results for a Gulf Coast year. During the year seven new oil fields, some of which are still of very little importance, and one new gas area have been discovered. These fields are Tom Ball, Greta, Cleveland, Raisin and Garwood in Colorado County; Louise and Premont in Jim Wells County, and the new producing gas area near Ace in southern Polk County. During the year salt has been found for the first time at Carlos and Esperson. New producing areas have been developed on East Stratton Ridge, Hockley, Hull, Port Neches, near Pettus in Bee County, and on the O'Connor Ranch in Victoria County. The total production for the Gulf Coast for the year was 62,837,435 bbl., an increase of 18,589,000 bbl. over 1932. During the year, 1307 wells have been drilled of which 207 were wildcats, compared with 653 wells and 141 wildcats the previous year. The total daily production at the end of the year was 165,201 bbl. At present there are 3100 oil wells producing. The average production per well is 55.5 bbl. per day. The price of crude fluctuated considerably during the year, beginning at 80c per barrel and closing the year at $1.04 per barrel. Completion data for 1933 are as follows:

Jan 1, 1934

By T. Sterry Hunt

In a paper presented to the Institute in 1881* I have discussed at some length the question of the " Hydrometallurgy of Copper," and among others, have noticed two methods, devised and patented by Mr. James Douglas and myself, for the extraction of copper

Jan 1, 1888

By W. P. Ward

I desire ho put on record a fact in relation to the effect of man ganese on pig iron which I have never seen in print, and which may, perhaps, not have been observed by anyone except myself. In 1875, while experimenting on the production of ferroman ganese in a blast furnace, I had burdened the furnace with a charge which I calculated would produce a 15-per cent. spiegel. The fur nace was very hot, having been running for a couple of days on a very light burden, and making a burnt iron, preparatory to the experiment I proposed to make to produce a high grade of spiegel. I calculated that the charge would begin to work in the fur nace in about twelve hoars after it was put on. After the -lapse of that time I commenced to watch the furnace carefully, but found little or no change in the appearance of the metal, although there was a very decided change in the cinder, showing that the man ganese ore had come in work. The iron was quite gray and very tough. The character of the cinder was good for a spiegel cinder, and 1 could not imagine where the manganese was going to, as it (lid not appear to be in either metal or cinder in anything like the quan tity indicated by the charge. The next morning things were still in the same condition. The furnace was very hot, the cinder good, and the iron very gray. I was then sorely puzzled. I had never heard of a gray iron with over 4 or 6 per cent. of manganese, and had no notion that an iron with more manganese could be gray and tough. With great difficulty a piece for chemical test was broken from a pig. Not less than a hundred blows from a heavy sledge were required to break it off, I took the specimen to the shop and directed that some borings from it should be brought to the laboratory, as soon as possible, whither I myself at once repaired to put things in readi ness for a rapid manganese determination. In about half an hour the machinist came in with the iron specimen in one hand and about a dozen blunted and broken steel drills in the other, saying that it mas impossible to drill the iron. There were several little depressions in the iron, which was malleable enough to be indented by the point of the drill, but not a chip had been cut from it. The metal was never subjected to further physical tests. A chip broken from

Jan 1, 1882

By Gustav S. Preller, A. M. Gaudin

Fox the past 20 years it has been generally accepted that the flotation process is made possible as a result of the action of certain chemical substances on the surface of the mineral particles. In fact, it has been suspected, but never demonstrated, that this action produces on the mineral particles a layer of chemosorbed ions that is of the order of magnitude of a monolayer; that is, of a layer one ion deep. It is the purpose of this paper to present certain initial results on the relationship of mineral surface area and collecting-agent requirements. Up to about eight years ago, all considerations involving the surface area of finely divided solids were-limited by the fact that there was not in existence any general method for determining the extent of such surfaces, especially on mixed materials. However, the method invented by Brunauer, Emmett and Teller1 has changed the situation by providing a general procedure (BET method). This procedure has already been applied to mineral dressing problems2 -4 and has now received confirmation as to accuracy by an entirely independent method.5 This confirmatory or "absolute" method uses a very tedious calorimetric procedure and is not suitable for routine determinations; but still another method6 now is available to relate the results obtained by the BET method to those obtained calorimetrically. This Harkins-Jura method has the advantage that it does not require an assumption concerning the parking area per molecule of adsorbate (nitrogen). In the original work by Brunauer, Emmett and Teller the parking area per nitrogen molecule was calculated to be either 13.8Å2. or 16.2Å2. according as the nitrogen was assumed to be closely packed as in crystalline nitrogen or loosely packed as in liquid nitrogen. The initial experimental work from this laboratory2 supported the 13.8Å2. figure; that work was done on glass spheres of measurable geometric area and it was based on the assumption that the glass spheres were truly smooth; any deviation from this assumption would, of course, have made the calculated parking area higher. Harkins and Jura's results suggest that the parking area is not the same for all substrata; furthermore, the average of the 87 measurements cited indicates a "preferred" parking area for the nitrogen molecule of about 15.2Å2., with extreme values at 13.7 and 16.9Å2. The average of 21 determinations made in connection with this study' gave a parking area of 14.3 ± 0.27Å2. In view of this result and of the Harkins and Jura

Jan 1, 1946

By G. K. Manning, C. H. Lorig

Two metallurgical tools have acquired wide use within the past several years as a means of studying the transformation characteristics of steel. One is a technique used first by Bain and Davenport for determining the transformation characteristics of a steel at constant temperature; the second is the end-quench hardenability test. Constant-temperature transformation curves like those of Bain and Davenport have done much to rationalize the metal¬lography of steel; however, in commercial practices, constant-temperature transformation is seldom encountered, therefore only rarely can such curves be directly applied. The real reason for the determination of such curves lies, in the fact that they provide a way of thinking about transformation that is both convenient and productive. The end-quench hardenability test is a more practical means of studying transformation, for, by correlating positions on the hardenability bar with shapes of different masses, an almost direct application of the results can be made. Unfortunately, the end-quench test, though practical, can do very little toward improving the metallurgists' way of thinking about transformation. These two metallurgical tools, dealing with precisely the same phenomenon, should be very closely associated in metallurgists' minds. Actually, they are frequently pushed into separate mental corners and considered as being more or less distinct and unrelated. The reason for this is that no strong connecting link between them has been developed. An attempt is sometimes made to relate these two tools by projecting the critical cooling rate on the isothermal transformation plot as illustrated in Fig. I. The critical cooling rate is considered as a constant rate-though in practical applications, cooling rates are never constant-and this constant cooling rate is given uniform significance from the Ae temperature down to the temperature of initial transformation. A little thought indicates the errors of such a procedure. Certainly the time interval spent just below point A of Fig. I cannot be as effective in promoting nucleation as is the time interval spent just above point B. Yet the procedure represented in Fig. I considers all the time spent between temperatures A and B to be just as effective in promoting nucleation as though all the time were spent at temperature B. Furthermore, change the shape of the isothermal curve between points B and C in any way desired, and the required critical cooling rate is not changed one iota. This cannot possibly be true. Such a way of thinking about critical cooling rates not only is incapable of giving any results that are quantitatively satisfactory but is likely to give very misleading qualitative results.

Jan 1, 1946

By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949

By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949

By W. A. Binsacca

The concentrator treats sulfide ore containing lead, copper, zinc, gold and silver, at the rate of 850 tons per 24 hr., and produces lead, copper, zinc and iron concentrates by selective flotation methods. The ore occurs below the oxidized zone along a main fracture, the wall rock of which is either greywacke or calcareous shale. The predominating sulfide minerals are galena, sphalerite, pyrite and chalcopyrite; the others are quartz and calcite. In minor amounts, arsenopyrite, pyrrhotite and hematite occur, and such secondary minerals as smithsonite, chalcocite, covellite, bornite, cerussite and anglesite are detected in the ore, the last two named occurring principally as surface alterations of the galena. The ore is hauled from the mine bins in 10-ton cars which pass over the track scales before entering the car dumper ahead of the crusher plant.&apos; A conveyor belt delivers the crushed ore to the sulfide bin, which has a capacity of 2800 tons. The primary grinding unit consists of two 6 by 12-ft. Marcy rod mills operating in parallel and in open circuit, each taking 425 tons per day. One rod mill discharges into an 8 by 25-ft. Dorr classifier with a 12-ft. bowl and the other into a 6 by 25-ft. Dorr duplex classifier. These classifiers are arranged so that each unit rakes the sands into a 6 by 14-ft. Traylor ball mill, which discharges to the bowl classifier only. The duplex classifier therefore operates in open circuit and the bowl classifier in closed circuit, the overflow of both classifiers furnishing the feed for the flotation section. Other groupings have been tried, but this has been found the most satisfactory. The Marcy mills are driven by 150-hp. slip-ring induction motors with speed reducers to give 17 r.p.m. The Traylor mill operates at a speed of 24 r.p.m. and is driven by a 200-hp. slip-ring induction motor, direct connected to pinion and gear. The bowl classifier operates at a speed of 22 r.p.m., with the bowl rake making 4.5 r.p.m. and the duplex classifier at 31 r.p.m. High-carbon steel rods of Mexican manufacture, 12 ft. long by 3-in. diameter, are used in the Marcy mills, with a resulting consumption of 1.52 Ib. per ton ore. The Traylor mill is fed 3-in. cast-iron balls cast in

Jan 1, 1935

By B. S. Blakeney, E. P. Abrahamson II

The effect of the transition elements in binary solid-solution additions upon the recrystallization temperature of iron has been investigated. All these elements immediately raised the temperature, the majority having their greatest effect in less than 0.10 at. pct. A correlation is noted between the rate of change of recrystallization temperature with atomic percent solute and the electron configuration of the solute element. THE work of Abrahamson and rant&apos; on binary chromium-base alloys indicated that a correspondence existed between the effect of each solute element on the brittle-to-ductile transition temperature of chromium and the ground-state electron configuration of the element added. This was felt to be a bonding phenomenon and would be expected to be observed in measurements of other properties involving the breaking or exchange of atomic bonds. From this work it was postulated that a like correspondence should be found for other properties of binary alloys, such as recrystallization. This study is an effort to check this postulation using binary solid-solution iron-base alloys. Previously, the majority of recrystallization studies were carried out on steels. However, Tammann2 investigated the recrystallization of iron as effected by Co, Ni, Si, Mn, Mo, and Cr and stated that elements with the same crystal structure at room temperature as iron appeared to be more effective in raising the recrystallization temperature. Austin, Luini, and Lindsay3 studied the effects of Ni, Cr, Mn, Co, Si, and Mo on cold rolling and annealing, but noted no trend. Abrahamson and rant,&apos; in their work on the effect of both substitutional and interstitial elements upon the brittle-to-ductile transition of chromium, have shown that the outer electron configuration in the ground state of the solute element appears to be the prime determinant of the transition temperature. PROCEDURE All alloys were made using 99.95 + pct Fe with 0.02 wt pct 0, 0.004 pct C, and 0.001 pct N. All alloying elements were 99.9 + percent pure. Metal-lographically the alloys, out to at least 0.1 at. pct, appeared to be in solid solution. Though several published phase diagrams tend to dispute this.4 All alloys were arc melted six times and cast into square 400-g ingots under an argon atmosphere.

Jan 1, 1961